That seems to be a common problem for Google’s management when it
comes to Google+:

Michael DeGusta

Only 3 of the 12 people listed on the Google
Management Team page have ever made a single public post on
Google+, totaling just 29 posts ever and only 6 in September.

It doesn’t stop with the board and the high level management.
Going one level down to the 6 Senior Vice Presidents
anointed in Larry Page’s reorganization last April still
reveals a lack of engagement: 4 of the 6 SVPs have made no posts
since August and they’ve managed only 9 posts ever, all but 1 of
which were by Andy
Rubin.

In total, of the 18 most senior people charged with overseeing
Google, 11 have either not joined or have never made a single
public post, and 5 have barely used it at all. Only Senior VP of
Social / head of Google+ Vic
Gundotra and SVP of ChromeSundar
Pichai have made any effort to seriously adopt Google+.

The Raw Data

Here’s the full table of public posts since the beginning of
Google+. Note that I’m counting a photo album as 1 sharing event
and also that Vic Gundora’s posts page seems to fail if you try
to go back past mid-July, hence the data gap there.

Pre-emptive Responses

1. “Google+ isn’t just about public sharing”

No, it’s not. But one of the key distinguishing features of
Google+ is combining Facebook-style private sharing / friending
with Twitter-style public posts / following. Even Facebook has
now emulated this and Facebook’s management is far more
active on their public feeds than Google is on theirs.

Further, I think it’s reasonable to assume a correlation between
private use & public use: if you were constantly posting
things on a service and each time you were given the option to
make it public or private, surely sometimes you’d make it public,
especially as a somewhat public figure wanting to help your own
company’s new service get going.

2. “The board/top management shouldn’t be expected to use
Google+”

Yes, they should - maybe not every member extensively, but not
even a single post by a single non-executive member of the board?
Can you imagine Fred Wilson not
publicly using the major new product of one of his companies?